Induction logging measurements are sensitive to water saturation and brine concentration in the rock pores. In an active reservoir, the formation's petrophysical parameters can have a strong imprint on the temporal and spatial distribution of water saturation and salt concentration, which in turn can be transformed into the distribution of formation conductivity using an appropriate saturation-resistivity equation. This relationship between induction measurements and the petrophysical parameters offers an opportunity to integrate electromagnetics and multi-phase fluid flow to provide a robust, physically consistent interpretation for reservoir characterization.
Induction logging tools can be used to determine the formation resistivity and invasion profile via a model-based inversion approach. See, Habashy, T. M. and A. Abubakar, 2004, A general framework for constraint minimization for the inversion of electromagnetic measurements: Progress In Electromagnetics Research, 46, 265-312 (hereinafter “Habashy and Abubakar”); Barber, T., B. Anderson, A. Abubakar, T. Broussard, K. Chen, S. Davydycheva, V. Druskin, T. Habashy, D. Homan, G. Minerbo, R. Rosthal, R. Schlein, and H. Wang, 2004, Determining formation resisitivty anisotropy in the presence of invasion, in SPE Annual Technical Conference and Exhibition, paper 90526; Abubakar, A., T. M. Habashy, V. Druskin, L. Knizhnerman, and S. Davydycheva, 2006, A 3d parametric inversion algorithm for triaxial induction data: Geophysics, 71, G1-G9; and Abubakar, A., T. M. Habashy, V. Druskin, and L. Knizhnerman, 2006, An enhanced gauss-newton inversion algorithm using a dual-optimal grid approach: IEEE Transactions on Geoscience and Remote Sensing, 44, 1419-1427. However, this application is constrained by some simplifying assumptions, for example, assuming a well penetrating a layer-cake formation with a step-profile three-parameter (Rxo, Rt, Di) invasion model. The quality and accuracy of the inversion results are affected by the complexity of the reservoir configuration and the actual invasion profile. In horizontal or highly deviated wells or in anisotropic formations, invasion profiles become too complex to be described by a simple invasion model. An alternative inversion approach is to employ the so-called pixel-based inversion method. See: Abubakar, A. and P. M. van den Berg, 2000, Nonlinear inversion in electrode logging in a highly deviated formation with invasion using an oblique coordinate system: IEEE Transactions on Geoscience and Remote Sensing, 38, 25-38; Alumbaugh, D. and M. Wilt, 2001, A numerical sensitivity study of three-dimensional imaging from a single borehole: Petrophysics, 42, 19-31; Abubakar, A. and P. van den Berg, 2002, Application of a non-orthogonal coordinate system to inverse single-well electromagnetic logging problem: Three-Dimensional Electromagnetics, eds. M. S. Zhdanov and P. E. Wannamaker, 215-231; Abubakar, A. and T. Habashy, 2006, Three-dimensional single-well imaging of the multi-array triaxial induction logging data, in SEG Technical Program Expanded Abstracts, volume 25, 411-415. A disadvantage of this pixel-based inversion method is that the number of unknowns used to describe the configuration is large and hence, a large number of unknown model parameters often need to be inverted. This approach will only provide a qualitative inverted resistivity map (an image) around the well-bore.
On the other hand, the mud-filtrate invasion affects the interpretation of well testing or wireline formation test. Although some researchers studied and discussed the influence of invasion to the formation test interpretation, practically, the interpretation of formation test usually still employs a single-phase fluid flow model regardless of the mud-filtrate invasion. The error associates with this can be neglected only when the mobility of the mud-filtrate is very close to that of the formation fluid and the capillary pressure is negligible or the invaded mud-filtrate has already been cleaned up from the test target zone by a drawdown, which may be time-consuming. A more realistic invasion profile will benefit both induction data interpretation and formation test interpretation.
Some previous works have already exploited the benefit of integrating the electromagnetic model with the multiphase fluid flow model. In Semmelbeck, M. E. and S. A. Holditch, 1988, The effects of mud-filtrate invasion on the interpretation of induction logs: SPE (hereinafter “Semmelbeck and Holditch (1988)”), an attempt is made to develop a model to simulate the mud-filtrate invasion process, which deals with the mud-cake and the formation simultaneously, and incorporated the capability to simulate the salt transport to calculate the formation resistivity. This model was then used to analyze the effect of the mud-cake permeability, the formation permeability, the porosity and the overbalance pressure on the induction logging data. In Tobola, D. P. and S. A. Holditch, 1991, Determination of reservoir permeability from repeated induction logging: SPE Formation Evaluation, 20-26 (hereinafter “Tobola and Holditch (1991)”), the approach described in Semmelbeck and Holditch (1988) was applied to a low permeability reservoir and determined the reservoir permeability by history matching the change in the induction logging data over time. The effect of the initial water saturation on the induction logging data was also analyzed. In this approach, the mud-cake permeability profile over time must be accurately simulated to properly interpret the induction logging data. In Yao, C. Y. and S. A. Holditch, 1996, Reservoir permeability estimation from time-lapse log data: SPE Formation Evaluation, 69-74 (hereinafter “Yao and Holditch (1996)”), the approach described in Semmelbeck and Holditch (1988) was extended to history match both the time-lapse resistivity and neutron logging data. This technique was used to estimate the reservoir permeability, which was verified against production data and core analysis.
The approaches described in Semmelbeck and Holditch (1988), Tobola and Holditch (1991) and Yao and Holditch (1996) simulate the mud-filtrate invasion assuming a mud-cake with a constant thickness and a variable permeability, which need to be accurately determined from other independent measurement data. See: Ferguson, C. K. and J. A. Klotz, 1954, Filtration from mud during drilling: Trans., AIME 201, 29-42; and Williams, M. and G. E. Cannon, 1938, Evaluation of filtration properties of drilling muds: The Oil Weekly, 25-32. These approaches ignore gravity and diffusion effects, and aim to estimate the permeability in tight formations. However, this estimation heavily depends on the precision of determining mud-cake properties, which is another difficult problem to be resolved.
Semmelbeck, M. E., J. T. Dewan, and S. A. Holditch, 1995, Invasion-based method for estimating permeability from logs: SPE 30581 presented at the 1995 SPE Annual Technical Conference and Exhibition, Dallas, 22-25 describes an extension of their previous work to integrate the fluid flow model with the Dewan's mudcake growth model, which is an experimentally-verified model for predicting the mud-cake thickness and the permeability during static and dynamic filtration conditions. See: Dewan, J. T. and M. E. Chenevert, 1993, Mudcake buildup and invasion in low permeability formations: application to permeability determination by measurement while drilling: SPWLA 34th Annual Logging Symposium, 13-16. This approach was applied to the new generation of array induction logging data. From a linear covariance analysis, they concluded that their method could provide reasonable estimates of the permeability in low to moderate permeable formations, but the method could not provide accurate estimates of the saturation-dependent properties.
Ramakrishnan, T. S. and D. J. Wilkinson, 1997, Formation producibility and fractional flow curves from radial resistivity variation caused by drilling fluid invasion: Physics of Fluids, 9, 833-844, and Ramakrishnan, T. S. and D. J. Wilkinson, Water-cut and fractional flow logs from array-induction measurements: SPE Reservoir Evaluation & Engineering, 2, 85-94 discuss establishing a mathematical model to estimate the fractional flow and the relative permeability curves from the array induction logging measurements. Based on the work described in the two Ramakrishnan papers, Zeybek, M., T. Ramakrishnan, S. AI-Otaibi, S. Salamy, and F. Kuchuk, 2001, Estimating multiphase flow properties using pressure and flowline water-cut data from dual packer formation tester interval tests and openhole array resistivity measurements: SPE 71568 discusses a methodology for estimating the horizontal and vertical layer permeabilities and the relative permeabilities using array induction logging tool measurements, pressure transient measurements and water-cut measurements from a packer-probe wireline formation tester. This joint inversion was done in a sequential mode. In this method, fractional flow parameters (connate water saturation, residual water saturation, maximum residual oil saturation, filtrate loss and pore size distribution) are estimated by matching resistivity measurements. These estimated fractional flow parameters are then input into a numerical model for the sampling process to ultimately match the observed and simulated water cut and pressure data. The final outputs are the relative, the horizontal and vertical permeabilities.
Alpak, F. O., T. M. Habashy, C. Torres-Verdin, and V. Dussan, 2004, Joint inversion of pressure and time-lapse electromagnetic logging measurements: Petrophysics, 45, 251-267 (hereinafter “Alpak, et al. (2004)”); Alpak, F. O., C. Torres-Verdin, and T. M. Habashy, 2004, Joint inversion of pressure and dc resistivity measurements acquired with in-situ permanent sensors: a numerical study: Geophysics, 69, 1173-1191; Alpak, F. O., C. Torres-Verdin, and T. M. Habashy 2006, Petrophysical inversion of borehole array-induction logs: Part I-numerical examples: Geophysics, 71, F101-F119; and Alpak, F. O., C. Torres-Verdin, T. M. Habashy, and K. Sephernoori, 2004, Simultaneous estimation of in-situ multiphase petrophysical properties of rock formations from wireline formation tester and induction logging measurements: SPE 90960 all discuss the simultaneous estimation of in-situ multiphase petrophysical properties of rock formations from wireline formation tester and induction logging measurements. The papers also discuss extensive work to assess the sensitivity of array induction measurements to the presence of the water-based mud-filtrate invasion for various combinations of petrophysical parameters and fluid properties. Torres-Verdin, C., F. O. Alpak, and T. M. Habashy, 2006, Petrophysical inversion of borehole array-induction log: Part II-field data examples: Geophysics, 71, G261-G268; and Salazar, J. M., C. Torres-Verdin, F. O. Alpak, T. M. Habashy, and J. D. Klein, 2006, Estimation of permeability from borehole array induction measurements: Application to the petrophysical appraisal of tight gas sands: Petrophysics, 47, 527-544 discuss applying method described by Alpak to some low or moderate permeability gas reservoirs for estimating the permeability and the porosity. This method employs a modified UTCHEM code (INVADE) (see Wu, J., C. Torres-Verdin, K. Sepehrnoori, and M. Proett, 2005, The influence of water-base mud properties and petrophysical parameters on mudcake growth, filtrate invasion, and formation pressure: Petrophysics, 46, 14-32) to calculate the time-dependent mud-filtrate loss rate, and takes the average of this rate as the injection rate to run a two-phase three-component fluid flow model for simulating the mud-filtrate invasion process, which consequently affects the resistivity measurements. Therefore, the accuracy of the inverted petrophysical parameters can depend on the mud-filtrate loss calculation, which is still a difficult problem at present. Angeles, R., J. Skolnakorn, F. Antonsen, A. Chandler, and C. Torres-Verdin, 2008, Advantages in joint-inversions of resistivity and formation-tester measurements: Examples from a norwegian field: SPWLA 49th Annual Logging Symposium, Edinburgh, Scotland discusses advancing previous work by using a reservoir simulator dynamically-coupled to a mud-filtrate invasion model. Hence they integrated the calculation of mud-filtrate invasion rate into the inversion process.
Pereira, N., R. Altman, J. Rasmus, and J. Oliveira, 2008, Estimation of permeability and permeability anisotropy in horizontal wells through numerical simulation of mud filtrate invasion: Rio Oil & Gas Expo and Conference, Rio de Janeiro. discusses an approach to estimate formation permeability and permeability anisotropy using dual inversion of time-lapse azimuthal laterolog-while-drilling and near well-bore numerical simulation of the water-based mud-filtrate invasion. This method requires a priori bottom hole pressure while drilling and assumes a known constant mud-cake permeability. Kuchuk, F., L. Zhan, S. M. Ma, A. M. Al-Shahri, T. S. Ramakrishnan, B. Altundas, M. Zeybek, R. Loubens, and N. Chugunov, 2008, Determination of in-situ two-phase flow properties through downhole fluid movement monitoring: SPE 116068 presented at the 2008 SPE Annual Technical Conference and Exhibition held in Denver, Colo., USA, 21-24 discusses method for in-situ estimation of two-phase transport properties of porous media using the time-lapse DC resistivity data, pressure and flow rate data. The time-lapse DC resistivity are recorded using a permanent downhole electrode resistivity array. The pressure and flow rate data are obtained from the injection test regardless of the mud-filtrate invasion. The integrated interpretation is based on an inversion workflow, which employs a multi-layered integrated flow/electrical numerical simulator to solve the fluid flow, the salt transport and the DC electrical array response. A field experiment conducted in a carbonate reservoir has been used to verify the proposed method.
Most of the above works involve the simulation of the mud-filtrate invasion process to obtain the invasion rates as accurately as possible. However, the mud-filtrate invasion is a dynamic and complex process. It starts with a high invasion rate, which is mainly controlled by the overbalance pressure and the formation permeability when a well is drilled. After the mud-cake is formed, the invasion rate will tend to be controlled by the mud-cake since the permeability of mud-cake is normally much lower than that of the formation. There have been extensive works on the simulation of the mud-filtrate invasion process, which although possible, is still too complex for any practical application, especially when considering the complicated drilling and reaming conditions, such as the mud circulation rate, workover, mud-cake scraped by the tools, and so on.